Simulation of Elastic Tree-Like Dynamic Systems in Presence of External Holonomic Constraints

Authors: Gevorkian H.A. Published: 22.04.2020
Published in issue: #2(89)/2020  
DOI: 10.18698/1812-3368-2020-2-4-24

Category: Mathematics | Chapter: Differential Equations, Dynamic Systems, and Optimal Control  
Keywords: Newton --- Euler method, dynamic system, elastic tree-like systems, Lagrange multipliers, slider-crank mechanism, elastic connecting rod, deformations, holonomic constraint

Modern scientific literature pays close attention to the problems of optimal modeling of elastic dynamic systems. The symbolic-recursive model of Newton --- Euler method with the provision of computational algorithms with a degree of complexity proportional to the dimension of these systems, i.e., O(n), has been adapted for dynamic systems with open kinematic chains, in particular, for elastic manipulators. If dynamic systems have closed kinematic chains, it is extremely difficult to propagate the strategy of numerical analysis without the mass matrix inversion. Consequently, the task of optimal modeling of tree-like dynamic systems is reduced to the search for combined strategies that use the procedures of strategies with and without inversion of mass matrices simultaneously. The paper introduces a method of numerical dynamic analysis of elastic tree-like multilink systems, the method combining the procedure of inverting the mass matrix with the procedure of effective kinematic calculation, borrowed from the generalized Newton --- Euler method. An approximate dynamic analysis technique is proposed that fully reproduces the recursive procedures of the generalized Newton --- Euler method. The technique is confirmed to the extent that the period of inversion of these systems is less than the time of their full functioning, and the range of displacements during one cycle is less than the complete revolution of the mechanism. The use of the approximate method for the dynamic analysis of elastic mechanisms is considered using the example of a numerical dynamic calculation of a slider-crank mechanism with an elastic connecting rod


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